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About the nth-Root Codes: a Gröbner Basis Approach to the Weight Computation

In: Gröbner Bases, Coding, and Cryptography

Author

Listed:
  • Marta Giorgetti

    (University of Milano, Department of Mathematics)

Abstract

Recently some methods have been proposed to find the distance and weight distribution of cyclic codes using Gröbner bases (Sala in Appl. Algebra Engrg. Comm. Comput. 13(2):137–162, 2002; Mora and Sala in J. Symbolic Comput. 35(2):177–194, 2003). We identify a class of codes for which these methods can be generalized. We show that this class contains all interesting linear codes (i.e., with d≥2) and we provide variants and improvements.

Suggested Citation

  • Marta Giorgetti, 2009. "About the nth-Root Codes: a Gröbner Basis Approach to the Weight Computation," Springer Books, in: Massimiliano Sala & Shojiro Sakata & Teo Mora & Carlo Traverso & Ludovic Perret (ed.), Gröbner Bases, Coding, and Cryptography, pages 357-360, Springer.
    • Handle: RePEc:spr:sprchp:978-3-540-93806-4_20
    DOI: 10.1007/978-3-540-93806-4_20
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